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Theorems · Theorem · field theory

ConditionallyCompleteLinearOrderedField.inducedMap_zero

∀ (α : Type u_2) (β : Type u_3) [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [inst_3 : Field β]
  [inst_4 : ConditionallyCompleteLinearOrder β] [IsStrictOrderedRing β] [Archimedean α],
  ConditionallyCompleteLinearOrderedField.inducedMap α β 0 = 0
Defined in
Mathlib.Algebra.Order.CompleteField
Cited by
2 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderIsStrictOrderedRingFieldConditionallyCompleteLinearOrderIsStrictOrderedRingArchimedean
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ConditionallyCompleteLinearOrderedField.inducedAddHom · cited by 2ConditionallyCompleteLine…ConditionallyCompleteLinearOrderedField.inducedMap_nonneg · cited by 2ConditionallyCompleteLine…LinearOrderedField.inducedMap_zero · cited by 0LinearOrderedField.induce…LinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingNat.cast_zero · cited by 1870Nat.cast_zeroArchimedean · cited by 603ArchimedeanConditionallyCompleteLinearOrder · cited by 542ConditionallyCompleteLine…Rat.cast_zero · cited by 29Rat.cast_zeroConditionallyCompleteLinearOrderedField.inducedMap · cited by 28ConditionallyCompleteLine…ConditionallyCompleteLinearOrderedField.inducedMap_rat · cited by 4ConditionallyCompleteLine…ConditionallyCompleteLinearOr…CITED BYCITES

Cites9

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Cited by3

Results whose statement or proof uses this declaration.